Baffled, overwhelmingly, Zev. I find myself wondering whether you’re a member of a Jewish cult. “Leaven” is “yeast”. My understanding of the prohibition against “leavened products” is that it means “yeast bread”, “raised” products, not things like matzohs and soda crackers. And certainly not things like seeds.
The grain and seed in its natural form, Zev, I am TOTALLY baffled at hearing referred to as a “leavened product”. Yeast? What yeast?
Wheat, barley, oats, rye and spelt are just “seeds”. Millet and sunflower seeds are “seeds”, too. Why are millet and sunflowers permitted but wheat, barley, oats, rye, and spelt are not? Why isn’t corn (maize) mentioned? What about amaranth? What about rice? What about dried peas, which are also included in hamster mix? They’re seeds, too.
Is this an official Jewish thing, or is it just in your church, or your family? Got a cite for any of this? Do other people deprive their pets of their normal diet during Passover?
If you’re a farmer, do the farm animals have to have a special diet, too? Dogs and cats? What about parrots and parakeets, who also eat a mix of seeds, grains, and nuts, and who with their fast metabolism can survive for only a day without “real” food?
I have NEVER heard of this. At all…
And I have to say that it sounds cruel. 
Zev, animals need to eat what they need to eat. Hamsters need a good mix of seeds and grains, period, no matter what the humans are eating. They need proteins, fats, carbohydrates, and vitamins and minerals, same as people. If you want to be kind and humane to your pet, you will give him the diet he needs, and not require him to follow your religious dietary requirements.
If it’s just a “can’t have the stuff in the house” thing, then for heaven’s sakes, find a non-Jewish friend to keep the poor creature for you while you do your Passover thing. Since it’s a hamster, not a dog, he doesn’t have to feed it or walk it–you fill up the seed container and the water bottle, and all he has to do is put the cage in a quiet place and leave it alone.
How many years have you been doing this? To how many hamsters?
Geez… 